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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.10410 |
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| _version_ | 1866913991270334464 |
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| author | Ramaharo, Franck |
| author_facet | Ramaharo, Franck |
| contents | We derive the Kauffman bracket polynomial for the shadow of the Celtic link $CK_4^{2n}$ using two complementary approaches. The first approach uses a recursive relation within the Celtic framework of Gross and Tucker, based on diagrammatic identities. The second approach makes use of a 4-tangle algebraic framework: a fundamental tangle is concatenated with itself n times to form an iterated composite tangle, and the Kauffman bracket polynomial is computed by decomposing the state space with respect to the basis elements of the 4-strand diagram monoid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The bracket polynomial of the Celtic link shadow $CK_4^{2n}$ Ramaharo, Franck Geometric Topology Combinatorics 57M25, 05A19 We derive the Kauffman bracket polynomial for the shadow of the Celtic link $CK_4^{2n}$ using two complementary approaches. The first approach uses a recursive relation within the Celtic framework of Gross and Tucker, based on diagrammatic identities. The second approach makes use of a 4-tangle algebraic framework: a fundamental tangle is concatenated with itself n times to form an iterated composite tangle, and the Kauffman bracket polynomial is computed by decomposing the state space with respect to the basis elements of the 4-strand diagram monoid. |
| title | The bracket polynomial of the Celtic link shadow $CK_4^{2n}$ |
| topic | Geometric Topology Combinatorics 57M25, 05A19 |
| url | https://arxiv.org/abs/2508.10410 |